{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:H2Z4PEHGHLQEYHONCGMQFNFL4D","short_pith_number":"pith:H2Z4PEHG","canonical_record":{"source":{"id":"1805.08756","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-22T17:39:07Z","cross_cats_sorted":[],"title_canon_sha256":"8c4512555a49a924c15e5a0752e05c9e680733f79417e9d40a977daa18d04fc8","abstract_canon_sha256":"0be5a7573bf7180b806df651ec0fde82d49fa0860b4a68696a19c4f4135d1f93"},"schema_version":"1.0"},"canonical_sha256":"3eb3c790e63ae04c1dcd119902b4abe0cd6037adf6a807eb403e849bbca783ef","source":{"kind":"arxiv","id":"1805.08756","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.08756","created_at":"2026-05-17T23:55:03Z"},{"alias_kind":"arxiv_version","alias_value":"1805.08756v2","created_at":"2026-05-17T23:55:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08756","created_at":"2026-05-17T23:55:03Z"},{"alias_kind":"pith_short_12","alias_value":"H2Z4PEHGHLQE","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H2Z4PEHGHLQEYHON","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H2Z4PEHG","created_at":"2026-05-18T12:32:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:H2Z4PEHGHLQEYHONCGMQFNFL4D","target":"record","payload":{"canonical_record":{"source":{"id":"1805.08756","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-22T17:39:07Z","cross_cats_sorted":[],"title_canon_sha256":"8c4512555a49a924c15e5a0752e05c9e680733f79417e9d40a977daa18d04fc8","abstract_canon_sha256":"0be5a7573bf7180b806df651ec0fde82d49fa0860b4a68696a19c4f4135d1f93"},"schema_version":"1.0"},"canonical_sha256":"3eb3c790e63ae04c1dcd119902b4abe0cd6037adf6a807eb403e849bbca783ef","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:55:03.491182Z","signature_b64":"BYVGjnqf5+/eoYXivnQ6ChQZz3KhFpJc5DMmMcZ8OB21tKSiG/UAzay62u1wlDNsBla/aHbAZsyix60n5ICWDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3eb3c790e63ae04c1dcd119902b4abe0cd6037adf6a807eb403e849bbca783ef","last_reissued_at":"2026-05-17T23:55:03.490754Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:55:03.490754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1805.08756","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0JBBkl7zjXAjHsiT9hCn6Ndi4telGmM7tJIfIo8WOz+5RB0To2cYLxIoVShBRwBs/kzRzUbjgbtkLKt1TvX8Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:25:20.071290Z"},"content_sha256":"9a6e704a0dcc1f81cc1d0f59b1f42379c279f2642f8261647ef5fd785759565a","schema_version":"1.0","event_id":"sha256:9a6e704a0dcc1f81cc1d0f59b1f42379c279f2642f8261647ef5fd785759565a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:H2Z4PEHGHLQEYHONCGMQFNFL4D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Analysis of Sequential Quadratic Programming through the Lens of Riemannian Optimization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OC","authors_text":"Song Mei, Yu Bai","submitted_at":"2018-05-22T17:39:07Z","abstract_excerpt":"We prove that a \"first-order\" Sequential Quadratic Programming (SQP) algorithm for equality constrained optimization has local linear convergence with rate $(1-1/\\kappa_R)^k$, where $\\kappa_R$ is the condition number of the Riemannian Hessian, and global convergence with rate $k^{-1/4}$. Our analysis builds on insights from Riemannian optimization -- we show that the SQP and Riemannian gradient methods have nearly identical behavior near the constraint manifold, which could be of broader interest for understanding constrained optimization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08756","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:55:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"juGYYdIKI4PqDTSJZrxRlKpbr60GbWBNChfUKI5WginXDYtzIhE8e2AzAHn81zQt9CRNi2rXEIWdDmbAVQc2CA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T03:25:20.071942Z"},"content_sha256":"e4dc3c40cd210e15ffc8731d553b716f477d678bf4de35278e1b2b50f82a3b11","schema_version":"1.0","event_id":"sha256:e4dc3c40cd210e15ffc8731d553b716f477d678bf4de35278e1b2b50f82a3b11"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/H2Z4PEHGHLQEYHONCGMQFNFL4D/bundle.json","state_url":"https://pith.science/pith/H2Z4PEHGHLQEYHONCGMQFNFL4D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/H2Z4PEHGHLQEYHONCGMQFNFL4D/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T03:25:20Z","links":{"resolver":"https://pith.science/pith/H2Z4PEHGHLQEYHONCGMQFNFL4D","bundle":"https://pith.science/pith/H2Z4PEHGHLQEYHONCGMQFNFL4D/bundle.json","state":"https://pith.science/pith/H2Z4PEHGHLQEYHONCGMQFNFL4D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/H2Z4PEHGHLQEYHONCGMQFNFL4D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:H2Z4PEHGHLQEYHONCGMQFNFL4D","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0be5a7573bf7180b806df651ec0fde82d49fa0860b4a68696a19c4f4135d1f93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-22T17:39:07Z","title_canon_sha256":"8c4512555a49a924c15e5a0752e05c9e680733f79417e9d40a977daa18d04fc8"},"schema_version":"1.0","source":{"id":"1805.08756","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1805.08756","created_at":"2026-05-17T23:55:03Z"},{"alias_kind":"arxiv_version","alias_value":"1805.08756v2","created_at":"2026-05-17T23:55:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.08756","created_at":"2026-05-17T23:55:03Z"},{"alias_kind":"pith_short_12","alias_value":"H2Z4PEHGHLQE","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_16","alias_value":"H2Z4PEHGHLQEYHON","created_at":"2026-05-18T12:32:28Z"},{"alias_kind":"pith_short_8","alias_value":"H2Z4PEHG","created_at":"2026-05-18T12:32:28Z"}],"graph_snapshots":[{"event_id":"sha256:e4dc3c40cd210e15ffc8731d553b716f477d678bf4de35278e1b2b50f82a3b11","target":"graph","created_at":"2026-05-17T23:55:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We prove that a \"first-order\" Sequential Quadratic Programming (SQP) algorithm for equality constrained optimization has local linear convergence with rate $(1-1/\\kappa_R)^k$, where $\\kappa_R$ is the condition number of the Riemannian Hessian, and global convergence with rate $k^{-1/4}$. Our analysis builds on insights from Riemannian optimization -- we show that the SQP and Riemannian gradient methods have nearly identical behavior near the constraint manifold, which could be of broader interest for understanding constrained optimization.","authors_text":"Song Mei, Yu Bai","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-22T17:39:07Z","title":"Analysis of Sequential Quadratic Programming through the Lens of Riemannian Optimization"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.08756","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:9a6e704a0dcc1f81cc1d0f59b1f42379c279f2642f8261647ef5fd785759565a","target":"record","created_at":"2026-05-17T23:55:03Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0be5a7573bf7180b806df651ec0fde82d49fa0860b4a68696a19c4f4135d1f93","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OC","submitted_at":"2018-05-22T17:39:07Z","title_canon_sha256":"8c4512555a49a924c15e5a0752e05c9e680733f79417e9d40a977daa18d04fc8"},"schema_version":"1.0","source":{"id":"1805.08756","kind":"arxiv","version":2}},"canonical_sha256":"3eb3c790e63ae04c1dcd119902b4abe0cd6037adf6a807eb403e849bbca783ef","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3eb3c790e63ae04c1dcd119902b4abe0cd6037adf6a807eb403e849bbca783ef","first_computed_at":"2026-05-17T23:55:03.490754Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:03.490754Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BYVGjnqf5+/eoYXivnQ6ChQZz3KhFpJc5DMmMcZ8OB21tKSiG/UAzay62u1wlDNsBla/aHbAZsyix60n5ICWDA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:03.491182Z","signed_message":"canonical_sha256_bytes"},"source_id":"1805.08756","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9a6e704a0dcc1f81cc1d0f59b1f42379c279f2642f8261647ef5fd785759565a","sha256:e4dc3c40cd210e15ffc8731d553b716f477d678bf4de35278e1b2b50f82a3b11"],"state_sha256":"cd5e127fb6a4e7ed5e488122b054a17698508fb6fc528bf0889df4501672ae0b"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KSTA0EkFUz5aLcaKwzMI7v9RfEVoYFDbUltTK6DUJXUAIzoBdRHGwRJWbrwymT+YdoeMqLv6EMQlnAllgt5QBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T03:25:20.075334Z","bundle_sha256":"c072bd9fd54deb291adb235e7a9d31c1d79599d8133f88fa566dd01a2e4032d0"}}